We compute the fully differential rate for the Higgs-boson decay h→Zℓ+ℓ− , with Z→ℓ′+ℓ′− . For these processes we assume the most general matrix elements within an effective Lagrangian framework. The electroweak chiral Lagrangian we employ assumes minimal particle content and Standard Model gauge symmetries, but it is otherwise completely general. We discuss how information on new physics in the decay form factors may be obtained that is inaccessible in the dilepton-mass spectrum integrated over angular variables. The form factors are related to the coefficients of the effective Lagrangian, which are used to estimate the potential size of new-physics effects.